TY - JOUR
T1 - Numerical Solution of a Degenerate, Diffusion Reaction Based Biofilm Growth Model on Structured Non-Orthogonal Grids
AU - Md. Afsar Ali, Hermann J. Eberl & Rangarajan Sudarsan
JO - Communications in Computational Physics
VL - 3
SP - 695
EP - 741
PY - 2018
DA - 2018/05
SN - 24
DO - http://doi.org/10.4208/cicp.OA-2017-0165
UR - https://global-sci.org/intro/article_detail/cicp/12277.html
KW - Biofilms, degenerate diffusion, non-orthogonal grids.
AB - <p style="text-align: justify;">A previously developed semi-implicit method to solve a density dependent
diffusion-reaction biofilm growth model on uniform Cartesian grids is extended to
accommodate non-orthogonal grids in order to allow simulation on more complicated
domains. The model shows two non-linear diffusion effects: it degenerates where the
dependent solution vanishes, and a super-diffusion singularity where it approaches its
upper bound. The governing equation is transformed to a general non-orthogonal ξ−η
curvilinear coordinate system and then discretized spatially using a cell centered finite
volume method. The nonlinear biomass fluxes at the faces of the control volume cell
are split into orthogonal and non-orthogonal components. The orthogonal component
is handled in a conventional manner, while the non-orthogonal component is treated
as a part of the source term. Extensive tests showed that this treatment of the non-orthogonal
flux component on the control volume face works well if the maximum
deviation from orthogonality in the region of the grid where the biomass is growing
is within 15-20 degrees. This range of validity is smaller than the one obtained with
the same method for the simpler porous medium equation which is the standard test
problem for degenerate diffusion equation but does not have all of the features of the
biofilm model.</p>